CITY SURVEYING 131 



o 



in which h = contour interval; 



Ao = area included by surface contour; 

 A w = area included by lowest contour; 

 2 .A 1 = sum of areas of odd-numbered contours; 

 2 A z = sum of areas of even-numbered contours. 

 EXAMPLE. Let, in the accompanying illustration, h = 5 ft.; 

 Ao= 13,350 sq. ft., Ai = 8,100 sq. ft., Az = 4,280 sq. ft., A 3 

 = 1,925 sq. ft., and A4 = 520 sq. ft. Find the volume V. 



SOLUTION. By substituting the given values in the formula, 

 V = (13,350+4X8,100+4X1,925+2X4,280+520) = 104,217 

 cu. ft. 



When there is an odd number of prismoids, the last pris- 

 moid may be computed separately by multiplying one-half 

 the sum of its end areas by the contour interval. 



CITY SURVEYING 



LINEAR MEASUREMENTS 



The surveying work to be done by a city often requires a 

 great degree of precision, necessitating the employment of 

 special methods and instruments. 



Corrections for Temperature. The steel tape is the stand- 

 ard instrument for city work. The usual lengths are 50 and 

 100 ft. When a high degree of precision is required, correc- 

 tions for temperature, pull, and sag of the tape are necessary. 

 For such work, the temperature at which the tape is exactly 

 its graduated length should be determined by a test in a respons- 

 ible testing laboratory, such as the Bureau of Standards in 

 Washington, which for a small charge will furnish the constants 

 of temperatures and pull for any tape. 



Let this temperature be to, and let a line of the true length fo 

 be measured with a tape at a temperature t. The correction 

 for temperature is then equal to 

 c(t-to)l. 



